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182 GPS for Land Surveyors
9. The combined factor is used in SPCS conversion. How is the combined fac-
tor calculated?
a. Scale factor is multiplied by the elevation factor.
b. Scale factor is divided by the grid factor.
c. Grid factor added to the elevation factor and the sum is divided by 2.
d. Scale factor is multiplied by the grid factor.
10. Which of the following statements is correct?
a. Geodetic and astronomic latitudes are identical.
b. Geocentric and geodetic latitudes are the same.
c. Geocentric, astronomic, and geodetic latitudes are not the same and
have different values.
d. All three latitudes are the same.
11. Deflection of the vertical is what?
w a. Angle between the gravity vector and plumb line
w b. Angle between the plumb line and the line perpendicular to the ellipsoid
w c. The deviation of the declination of the instrument from the plumb line
d. The distance between the gravity vector and plumb line
.Ea 12. Orthomorphic map projection preserves what?
sy a. Azimuth and distance
E b. Angles and distances
n c. Areas and shapes
gi d. Directions and areas
neerANSWERS AND EXPLANATIONS
ing 1. Answer is (c)
. Explanation: With very slight changes, GRS80 became WGS84, which
neis the reference ellipsoid for the coordinate system, known as the World
tGeodetic System 1984 (WGS84). This datum has been used by the U.S.
Military since January 21, 1987, as the basis for the GPS Navigation mes-
sage computations. Therefore, coordinates provided directly by GPS receiv-
ers are based in WGS84. The newest incarnation of WGS84 is WGS84
(G1762). It was implemented by GPS Operational Control Segment in 2013.
2. Answer is (d)
Explanation: It took more than 10 years to readjust and redefine the
horizontal coordinate system of North America into what is now NAD83.
More than 1.7 million positions derived from classical surveying techniques
throughout the Western Hemisphere were involved in the least squares
adjustment. They were supplemented by approximately 30,000 EDM mea-
sured baselines 5000 astronomic azimuths, and 650 Doppler stations posi-
tioned by the TRANSIT satellite system. Over 100 Very Long Baseline
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Coordinates 183
Interferometry (VLBI) vectors were also included, but GPS, in its infancy,
contributed only five points.
3. Answer is (d)
Explanation: In the United States, state plane systems are based on the
transverse Mercator projection, an oblique Mercator projection, and the
Lambert conic map projection grid. Every state, Puerto Rico, and the U.S.
Virgin Islands have their own plane rectangular coordinate system.
4. Answer is (a)
Explanation: The geoid undulates with the uneven distribution of
the mass of the Earth and has all the irregularity that implies. In fact,
the separation between the bumpy surface of the geoid and the smooth
GRS80 ellipsoid varies from 0 up to 100 m. Therefore, the only way a
surveyor can convert an ellipsoidal height from a GPS observation on
wa particular station into a useable orthometric elevation is to know the
wextent of geoid-ellipsoid separation, also known as the geoid height, at
wthat point.
Toward that end, major improvements have been made over the past
.Equarter century or so in mapping the geoid on both national and global
ascales. This work has gone a long way toward the accurate determination
syof the geoid-ellipsoid separation, or geoid height, known as N. The formula
Efor transforming ellipsoidal heights h into orthometric elevations H is H =
nh – N.
gine 5. Answer is (a)
e Explanation: The geoid is a representation of the Earth’s gravity field. It
riis an equipotential surface that is everywhere perpendicular to the direction
ngof gravity. In other words, it is perpendicular to a plumb line at every point.
. Mean Sea Level is the average height of the surface of the sea for all
nestages of the tide. It was and sometimes still is used as a reference for eleva-
ttions. However, it is not the same as the geoid. Mean Sea Level departs from
the surface of the geoid; these displacements are known as the sea surface
topography. Neither is the ellipsoid, a smooth mathematically defined sur-
face, always parallel to the bumpy geoid. Finally, the geoid is certainly not
coincident with the topographic surface of the Earth.
6. Answer is (b)
Explanation: The creation of High-Accuracy Reference Networks
(HARN) was a cooperative venture between NGS and the states and often
included other organizations as well. With heavy reliance on GPS observa-
tions, these networks are intended to provide extremely accurate, vehicle-
accessible, regularly spaced control points with good overhead visibility.
To ensure coherence, when the GPS measurements are complete, they were
submitted to NGS for inclusion in a statewide readjustment of the existing
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184 GPS for Land Surveyors
NGRS covered by the state. Coordinate shifts of 0.3 to 1.0 m from NAD83
values have been typical in these readjustments.
7. Answer is (a)
Explanation: The UTM projection divides the world into 60 zones that
begin at λ 180°, each with a width of 6° of longitude, extending from 84° Nϕ
and 80° Sϕ. Its coverage is completed by the addition of two polar zones.
The coterminous United States are within UTM zones 10 to 19.
The UTM grid is defined in meters. Each zone is projected onto a cylin-
der that is oriented in the same way as that used in the transverse Mercator
state plane coordinates described above. The radius of the cylinder is cho-
sen to keep the scale errors within acceptable limits. Coordinates of points
from the reference ellipsoid within a particular zone are projected onto the
UTM grid.
The intersection of each zone’s central meridian with the equator defines
wits origin of coordinates. In the Southern Hemisphere, each origin is given the
wcoordinates: easting = X0 = 500,000 m and northing = Y0 = 10,000,000 m to
wensure that all points have positive coordinates. In the Northern Hemisphere,
.the values are easting = X0 = 500,000 m and northing = Y0 = 0 m at the
Eorigin. The scale factor grows from 0.9996 along the central meridian of a
aUTM zone to 1.00000 at 180,000 m to the east and west.
syE 8. Answer is (b)
n Explanation: The best geocentric reference frame currently available is
githe International Terrestrial Reference Frame (ITRF). Its origin is at the
necenter of mass of the whole Earth including the oceans and atmosphere.
eThe unit of length is the meter. The orientation of its axes was established
rias consistent with that of the IERS’s predecessor, Bureau International de
ngl’Heure (BIH), at the beginning of 1984.
. Today, the ITRF is maintained by the International Earth Rotation
neService (IERS), which monitors Earth Orientation Parameters (EOP) for
tthe scientific community through a global network of observing stations.
This is done with GPS, Very Long Baseline Interferometry (VLBI), Lunar
Laser Ranging (LLR), satellite laser ranging (SLR), Doppler Orbitography
and Radiopositioning Integrated by Satellite (DORIS), and the positions of
the observing stations are now considered to be accurate to the centimeter
level.
The ITRF is actually a series of realizations. In other words, it is revised
and published on a regular basis. Today NAD83 can be realizably defined
in terms of a best-fit transformation from ITRF96.
9. Answer is (a)
Explanation: The grid factor changes with the ellipsoidal height of the
line. It also changes with its location in relation to the standard lines of its
SPCS zone. The grid factor is derived by multiplying the scale factor by
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Coordinates 185
the elevation factor. The product is nearly 1 and is known as either the grid
factor or the combination factor. There is a different combination factor for
every line in the correct application of SPCS.
10. Answer is (c)
Explanation: One might expect that this astronomic latitude would be
the same as the geocentric latitude of the point, but they are different. The
difference is due to the fact that a plumb line coincides with the direction
of gravity; it does not point to the center of the Earth where the line used to
derive geocentric latitude originates.
11. Answer is (b)
Explanation: The angle between the vertical extension of a plumb line
and the vertical extension of a line perpendicular to the ellipsoid is called
the deflection of the vertical. It sounds better than the difference in down.
wThis deflection of the vertical defines the actual angular difference between
wthe astronomic latitude and longitude of a point and its geodetic latitude and
wlongitude; latitude and longitude because, even though the discussion has
so far been limited to latitude, the deflection of the vertical usually has both
.Ea north–south and an east–west component. The deflection of the vertical
aalso has an effect on azimuths; for example, there will be a slight difference
sybetween the azimuth of a GPS baseline and the astronomically determined
Eazimuth of the same line.
ngi 12. Answer is (b)
ne Explanation: Map projections in which shape is preserved are known as
econformal or orthomorphic. Orthomorphic means right shape. In a confor-
rimal projection the angles between intersecting lines and curves retain their
ngoriginal form on the map. In other words, between short lines, meaning
.lines under about 10 miles (about 16 km), a 45° angle on the ellipsoid is a
ne45° angle on the map. It also means that the scale is the same in all direc-
ttions from a point; in fact, it is this characteristic that preserves the angles.
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6 Static Global Positioning
System Surveying
Static Global Positioning System (GPS) surveying has been used on control surveys
from a local to statewide extent and will probably continue to be the preferred tech-
nique in that category. If a static GPS control survey is carefully planned, it usually
progresses smoothly. The technology has virtually conquered two stumbling blocks
that have defeated the plans of conventional surveyors for generations. Inclement
weather does not disrupt GPS observations, and a lack of intervisibility between sta-
tions is of no concern whatsoever, at least in post-processed GPS. Still, GPS is far
wfrom so independent of conditions in the sky and on the ground that the process of
wdesigning a survey can now be reduced to points-per-day formulas, as some would
like. Even with falling costs, the initial investment in GPS remains large by most
wsurveyors’ standards. However, there is seldom anything more expensive in a GPS
.Eproject than a surprise.
aStatic GPS was the first method of GPS surveying used in the field. Relative static
sypositioning involves several stationary receivers simultaneously collecting data from
Eat least four satellites during observation sessions that usually last from 30 min to
n2 hours. A typical application of this method would be the determination of vectors, or
gibaselines, between several static receivers to accuracies from 1 to 0.1 ppm over tens
nof kilometers. There are few absolute requirements for relative static positioning.
eeThe requisites include more than one receiver, four or more satellites, and a mostly
riunobstructed sky above the stations to be occupied. However, as in most of survey-
ning, the rest of the elements of the system are dependent on several other consider-
g.netations, and this implies planning.
PLANNING
A Few Words about Accuracy
When planning a GPS or Global Navigation Satellite System (GNSS) survey, one of
the most important parameters is the accuracy specification. A clear accuracy goal
avoids ambiguity both during and after the work is done. First, it is important to
remember that there is a difference between precision and accuracy.
One aspect of precision can be visualized as the tightness of the clustering of mea-
surements; the closer the grouping, the more precise the measurement. Accuracy,
however, requires one more element.
It has to have a truth set. For example, the truth in Figure 6.1 for a, b, and c is the
center of the target; without that, accuracy is indefinable. In other words, accuracy is
not determined by measurement alone. There must also be a standard value or values
187
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188 GPS for Land Surveyors
(a) (b) (c)
FIGURE 6.1 Precision and accuracy 1. (a) Accurate but not precise, (b) precise but not accu-
rate, and (c) accurate and precise.
involved. It is through the comparison of the measurements with such standard val-
ues that the outcome of the work can be found to be sufficiently near the ideal or true
wvalue, or not.
wFor example, in Figure 6.2a it may seem at first that the average of the measure-
wments in the GPS-A group are more accurate than the average of those in GPS-B
.because the GPS-A group is more precise. However, when the true position is intro-
Educed in Figure 6.2b, it is revealed that the GPS-B group’s average is the more accu-
asrate of the two, because accuracy and precision are not the same.
yWhen it comes to accuracy, there are other important details, too. Local accuracy
Eand network accuracy are not the same. As mentioned in Chapter 4, local accuracy,
ngalso known as relative accuracy, represents the uncertainty in the positions relative
ito the other adjacent points to which they are directly connected. Network accuracy,
nealso known as absolute accuracy, requires that a position’s accuracy be specified with
erespect to an appropriate truth set such as a national geodetic datum. Differentially
ricorrected GPS survey procedures that are tied to continuously operating reference
ngstations (CORS), which represent the National Spatial Reference System (NSRS) of
.netthe United States, provide information from which network accuracy can be derived.
GPS-A GPS-A
GPS-B GPS-B
True position
(a) (b)
FIGURE 6.2 Precision and accuracy 2. (a) GPS-A is more precise than GPS-B but (b) after
averaging GPS-B is more accurate than GPS-A.
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Static Global Positioning System Surveying
Vertical
uncertainty
Horizontal
uncertainty
wFIGURE 6.3 Horizontal and vertical accuracy.
wwHowever, autonomous GPS positioning, i.e., a single receiver without augmentation,
is not operating relative to any control, local or national. In that context it is more
.Eappropriate to discuss the precision of the results than it is to discuss accuracy.
asIt is typical for uncertainty in horizontal accuracies to be expressed in a number
ythat is radial. The uncertainties in vertical accuracies are given similarly, but they are
Elinear, not radial. In both cases the limits are always plus or minus (±) (see Figure 6.3).
ngIn other words, the reporting standard in the horizontal component is the radius of
ia circle of uncertainty, such that the true location of the point falls within that circle
neat some level of reliability, i.e., 95 percent of the time. Also, the reporting standard in
ethe vertical component is a linear uncertainty value, such that the true location of the
ripoint falls within ± of that linear uncertainty to some degree of reliability. In GPS
ngpositioning it is reasonable to expect that the vertical accuracy will be about 1/3 that
.of horizontal accuracy. In other words, if the absolute horizontal accuracy of a GPS
neposition is ±1 m, then the estimate of the absolute vertical accuracy of the same GPS
tposition would be approximately ±3 m.
Here is bit more on horizontal accuracy. Figure 6.4 shows a spread of positions
around a center of the range. As the radius of the error circle grows larger, the certainty
that the center of the range is the true position increases (it never reaches 100 percent).
Standards of Accuracy
The Federal Geodetic Control Committee (FGCC) wrote accuracy standards for
GPS relative positioning techniques. These were preceded by older standards of first,
second, and third order that then became subsumed under the group C in the newer
scheme. Until the last decades of the twentieth century, the cost of achieving first-
order accuracy was considered beyond the reach of most conventional surveyors.
Besides, surveyors often said that such results were far in excess of their needs any-
way. The burden of the equipment, techniques, and planning that is required to reach
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190 GPS for Land Surveyors
Circular error probable (CEP) = 50% = 0.5 m error circle radius = ±0.5 m
1-Sigma (1σ) = 68% = 0.6 m error circle radius = ±0.6 m
E90 = 90% = 0.9 m error circle radius = ±0.9 m
E95 = 95% = 1.0 m error circle radius = ±1.0 m
wwFIGURE 6.4 Horizontal point accuracy.
w.its 2σ relative error ratio of 1 part in 100,000 of the old first order was something
Emost surveyors were happy to leave to government agencies. However, the FGCC’s
astandards of B, A, and AA are respectively 10, 100, and 1000× more accurate than
syfirst order. With the advent of GPS the attainment of these accuracies did not require
Ecorresponding 10-, 100-, and 1000-fold increases in equipment, training, personnel,
nor effort. They were now well within the reach of private GPS surveyors both eco-
ginomically and technically. These accuracy standards are now superseded.
neIn 1998 the FGCC under the Federal Geographic Data committee published the
eGeospatial Positioning Accuracy Standards Part 2: Standards for Geodetic Networks
ri(FGDC 1998). These standards, shown in Table 6.1, supplant the earlier standards of
ng1984 and 1989.
.netNew Design Criteria
These upgrades in accuracy standards not only accommodate control by static GPS,
but they also have cast survey design into a new light for many surveyors. Nevertheless,
it is not correct to say that every job suddenly requires the highest achievable accu-
racy, nor is it correct to say that every GPS survey now demands an elaborate design.
In some situations, a crew of two or even one surveyor on-site may carry a GPS
survey from start to finish with no more planning than minute-to-minute decisions
can provide even though the basis and the content of those decisions may be quite
different from those made in a conventional survey.
In areas that are not heavily treed and generally free of overhead obstructions,
sufficient accuracy may be possible without a prior design of any significance. While
it is certainly unlikely that a survey of photocontrol or work on a cleared construc-
tion site would present overhead obstruction problems comparable with a static GPS
control survey in the Rocky Mountains, even such open work may demand prelimi-
nary attention. For example, just the location of appropriate vertical and horizontal
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Static Global Positioning System Surveying
TABLE 6.1
Accuracy Standards
Horizontal, Ellipsoid Height, and Orthometric Height
Accuracy Classification 95% Confidence (Less than or Equal to)
1-Millimeter 0.001 meters
2-Millimeter 0.002 meters
5-Millimeter 0.005 meters
1-Centimeter 0.010 meters
2-Centimeter 0.020 meters
5-Centimeter 0.050 meters
1-Decimeter 0.100 meters
2-Decimeter 0.200 meters
5-Decimeter 0.500 meters
1-Meter 1.000 meters
2.000 meters
w 2-Meter 5.000 meters
w5-Meter 10.000 meters
w10-Meter
.ESource: Federal Geographic Data Committee FGDC-STD-007.2-1998 Draft
aGeospatial Positioning Accuaracy Standards Part 2: Standard for
syGeodetic Networks.
Enginecontrol stations or obtaining permits for access across privately owned property or
egovernment installations can be critical to the success of the work.
ringLay of the Land
.neAn initial visit to the site of the survey is not always possible. Today, online map-
tping browsers are making virtual site evaluation possible as well. Topography as it
affects the line of sight between stations is of no concern on a static GPS project,
but its influence on transportation from station to station is a primary consideration.
Perhaps some areas are only accessible by helicopter or other special vehicle. Initial
inquiries can be made. Roads may be excellent in one area of the project and poor
in another. The general density of vegetation, buildings, or fences may open general
questions of overhead obstruction or multipath. The pattern of land ownership rela-
tive to the location of project points may raise or lower the level of concern about
obtaining permission to cross property.
Maps
Maps, both digital and hard copy, are particularly valuable resources for preparing
a static GPS survey design. Local government and private sources can sometimes
provide appropriate mapping, or it may be available online.
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192 GPS for Land Surveyors
NATIONAL GEODETIC SURVEY (NGS) CONTROL
NGS Control Data Sheets
Monuments that are the physical manifestation of the NSRS and can be occupied
with survey equipment are known as passive marks. They can provide reliable
control when properly utilized. That utilization should be informed by an under-
standing of the data sheet that accompanies each station and is easily available
online.
There is a good deal of information about the passive survey monuments on each
individual sheet (see Figure 6.5). In addition to the latitude and longitude, the pub-
lished data include the State Plane Coordinates in the appropriate zones. The first
line of each data sheet includes the retrieval date. Then the station’s category is
indicated. There are several, and among them are Continuously Operating Reference
Station, Federal Base Network Control Station, and Cooperative Base Network
Control Station. This is followed by the station’s designation, which is its name, and
wits Permanent Identifier (PID). Either of these may be used to search for the station
win the NGS database. The PID is also found all along the left side of each data sheet
wrecord and is always two uppercase letters followed by four numbers. The state,
.county, country, and U.S. Geological Survey (USGS) 7.5 minute quad name follows.
EEven though the station is located in the area covered by the quad sheet, it may not
asactually appear in the map. Under the heading, “Current Survey Control,” you will
yfind the latitude and longitude of the station in NAD83, which is fixed to the North
EnAmerican plate, currently, in NAD83 (2011), and its height in NAVD88. The ortho-
gmetric height in meters is listed as “ORTHO HEIGHT” and followed by the same in
infeet. When the height is derived from GPS observation, a geoid model must be used
eto determine the orthometric height. The model used is given.
eAdjustments to NAD27 and NGVD29 datums are a thing of the past. However,
rinthese old values may be shown under Superseded Survey Control. Horizontal val-
gues may be either scaled, if the station is a benchmark, or adjusted, if the station is
.nindeed a horizontal control point.
etWhen a date is shown in parentheses after NAD83 in the data sheet, it means
that the position has been readjusted. There are 13 sources of vertical control values
shown on NGS data sheets. Here are a few of the categories. There is adjusted, which
are given to three decimal places and are derived from least squares adjustment of
precise leveling. Another category is posted, which indicates that the station was
adjusted after the general NAVD adjustment in 1991. When a station’s elevation has
been found by precise leveling but nonrigorous adjustment, it is called computed.
Stations’ vertical values are given to one decimal place if they are from GPS obser-
vation (Obs) or vertical angle measurements (Vert Ang), and they have no decimal
places if they were scaled from topographic map, scaled, or found by conversion
from NGVD29 values using the program known as VERTCON.
When they are available, Earth-Centered-Earth-Fixed (ECEF) coordinates are
shown in X, Y, and Z. These are right-handed system, 3-D Cartesian coordinates and
are computed from the position and the ellipsoidal height. They are the same type
of X, Y, and Z coordinates presented in Chapter 5. These values are followed by the
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Static Global Positioning System Surveying
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FIGURE 6.5 NGS control data sheet.
(Continued)
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194 GPS for Land Surveyors
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FIGURE 6.5 (CONTINUED) NGS control data sheet.
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Static Global Positioning System Surveying 195
quantity that when added to an astronomic azimuth yields a geodetic azimuth and is
known as the Laplace correction. It is important to note that NGS uses a clockwise
rotation regarding the Laplace correction. The ellipsoid height per the NAD83 ellip-
soid is shown followed by the geoid height where the position is covered by NGS’s
GEOID program. The FGDC network accuracy is shown at a 95 percent reliability
level. Photographs of the station may also be available in some cases. When the data
sheet is retrieved online, one can use the link provided to bring them up. Also, the
geoidal model used is noted.
Coordinates
NGS data sheets also provide state plane and Universal Transverse Mercator (UTM)
coordinates, the latter only for horizontal control stations. State plane coordinates
are given in both U.S. Survey Feet or International Feet and UTM coordinates are
given in meters. Azimuths to the primary azimuth mark are clockwise from north
and scale factors for conversion from ellipsoidal distances to grid distances. This
winformation may be followed by distances to reference objects. Coordinates are not
wgiven for azimuth marks or reference objects on the data sheet.
wStation Mark
.EAlong with mark setting information, the type of monument and the history of mark
arecovery, the NGS data sheets provide a valuable to-reach description. It begins
sywith the general location of the station. Then starting at a well-known location, the
Eroute is described with right and left turns, directions, road names, and the distance
ntraveled along each leg in kilometers. When the mark is reached, the monument is
gidescribed and horizontal and vertical ties are shown. Finally, there may be notes
neabout obstructions to GPS visibility, and so forth.
eriSignificance of the Information
nThe value of the description of the monument’s location and the route used to reach
g.it is directly proportional to the date it was prepared and the remoteness of its loca-
netion. The conditions around older stations often change dramatically when the area
thas become accessible to the public. If the age and location of a station increases the
probability that it has been disturbed or destroyed, then reference monuments can be
noted as alternatives worthy of on-site investigation. However, special care ought to
be taken to ensure that the reference monuments are not confused with the station
marks themselves.
CONTROL FROM CONTINUOUSLY OPERATING NETWORKS
The requirement to occupy physical geodetic monuments in the field can be obviated
by downloading the tracking data available online from appropriate Continuously
Operating Reference Stations (CORS) where their density is sufficient. These sta-
tions, also known as active stations, comprise fiducial networks that support a vari-
ety of GPS applications. While they are frequently administered by governmental
organizations, some are managed by public-private organizations and some are
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196 GPS for Land Surveyors
commercial ventures. The most straightforward benefit of CORS is the user’s ability
to do relative positioning without operating his own base station by depending on
that role being fulfilled by the network’s reference stations.
While CORS can be configured to support differential GPS (DGPS) and real-
time kinematic applications, as in Real-Time Networks, most networks constantly
collect GPS tracking data from known positions and archive the observations for
subsequent download by users from the Internet.
In many instances, the original impetus of a network of CORS was geodynamic
monitoring as illustrated by the GEONET established by the Geographical Survey
Institute in Japan after the Kobe earthquake. Networks that support the monitor-
ing of the International Terrestrial Reference System (ITRS) have been created
around the world by the International GNSS Service (IGS), which is a service of
the International Association of Geodesy and the Federation of Astronomical
and Geophysical Data Analysis Services originally established in 1993. Also, the
Southern California Integrated GPS Network is a network run by a government–
wuniversity partnership.
wDespite the original motivation for the establishment of a CORS network, the
wresult has been a boon for high-accuracy GPS positioning. The data collected by
these networks is quite valuable to GPS surveyors around the world. Surveyors in
.Ethe United States can take advantage of the CORS network administered by the
aNational Geodetic Survey (NGS). The continental NGS system has two components,
sythe Cooperative CORS and the National CORS. Together they comprise a network
Eof hundreds of stations which constantly log multifrequency GPS data and make the
ndata available in the Receiver Independent Exchange (RINEX) format.
gineNGS Continuously Operating Reference Stations
eriNGS manages the National CORS system to support post-processing GPS data.
ngInformation is available in both code and carrier phase GPS data from receivers at
.these stations throughout the United States and its territories. That data can then be
neconveniently downloaded in its original form from the Internet free of charge for up
tto 30 days after its collection. It is also available later, but after it has been decimated
to a 30 s format.
The Cooperative CORS system supplements the National CORS system. The
NGS does not directly provide the data from the cooperative system of stations. Its
stations are managed by participating university, public, and private organizations
that operate the sites.
Nearly all coordinates provided by NGS for the CORS sites are available in
NAD83 (2011) epoch 2010.0. The coordinates of CORS stations are also published
in IGS08. However, these positions differ from NAD83 (2011). GPS observations are
the foundation of IGS08, which is consistent with ITRF08. The coordinates in both
NAD83 (2011) and IGS08 are accompanied by velocities because they are moving.
An IGS08 position may differ slightly for a station, but the velocities for both refer-
ence frames are identical. These velocities can be used to calculate the stations posi-
tion at a different date using NGS’s Horizontal Time Dependent Positioning (HTDP)
utility.
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Static Global Positioning System Surveying 197
NGS CORS Reference Points
At a CORS site, NGS provides the coordinates of the L1 phase center and the Antenna
Reference Point (ARP). Generally speaking, it is best to adopt the position that can
be physically measured, that means the coordinates given for the ARP. It is the coor-
dinate of the part of the antenna from which the phase center offsets are calculated
that is usually the bottom mount.
The phase centers of antennas are not immovable points. They actually change
slightly, mostly as the elevation of the satellite’s signals change. In any case, the
phase centers for L1, L2, and L5 differ from the position of the ARP both vertically
and horizontally. NGS provides the position of the phase center on average at a par-
ticular CORS site. As most post-processing software will, given the ARP, provide
the correction for the phase center of an antenna, based on antenna type, the ARP is
the most convenient coordinate value to use.
wInternational Global Navigation Satellite System (GNSS) Service (IGS)
wLike NGS, IGS also provides CORS data. However, it has a global scope. The infor-
wmation on the individual stations can be accessed including the ITRF00 Cartesian
.Ecoordinates and velocities for the IGS sites, but not all the sites are available from
aIGS servers. The Scripps Orbit and Permanent Array Center is a convenient access
sypoint for IGS data. A virtual map of the available GPS networks can be found there.
EngSTATIC SURVEY PROJECT DESIGN
inThe selection of satellites to track, start and stop times, mask elevation angle, assign-
eement of data file names, reference position, bandwidth, and sampling rate are some
rioptions useful in the static mode, as well as other GPS surveying methods. These
nfeatures may appear to be prosaic, but their practicality is not always obvious. For
g.example, satellite selection can seem unnecessary when using a receiver with suffi-
necient independent channels to track all satellites above the receiver’s horizon without
tdifficulty. However, a good survey project design pays dividends by limiting lost
time and maximizing productivity.
Horizontal Control
When geodetic surveying was more dependent on optics than electronic signals from
space, horizontal control stations were set with station intervisibility in mind, not
ease of access. Therefore, it is not surprising that stations established in that way are
frequently difficult to reach. Not only are they found on the tops of buildings and
mountains, but they are also in woods, beside transmission towers, near fences, and
generally obstructed from GPS signals. The geodetic surveyors that established them
could hardly have foreseen a time when a clear view of the sky above their heads
would be crucial to high-quality control.
In fact, it is only recently that most private surveyors have had any routine use
for NGS stations. Many station marks have not been occupied for quite a long time.
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198 GPS for Land Surveyors
Because the primary monuments are often found deteriorated, overgrown, unstable,
or destroyed, it is important that surveyors be well acquainted with the underground
marks, reference marks, and other methods used to perpetuate control stations.
Obviously, it is a good idea to propose reconnaissance of several more than the
absolute minimum of three horizontal control stations. Fewer than three makes any
check of their positions virtually impossible. Many more are usually required in
a GPS route survey. In general, in GPS networks, the more well-chosen horizon-
tal control stations available, the better. Some stations will almost certainly prove
unsuitable unless they have been used previously in GPS work.
Station Location
The location of the stations, relative to the GPS project itself, is also an important
consideration in choosing horizontal control. For work other than route surveys, a
handy rule of thumb is to divide the project into four quadrants and to choose at least
wone horizontal control station in each. The actual survey should have at least one
whorizontal control station in three of the four quadrants. Each of them ought to be
was near as possible to the project boundary. Supplementary control in the interior of
the network can then be used to add more stability to the network (see Figure 6.6).
.EAt a minimum, route surveys require horizontal control at the beginning, the end,
aand the middle. Long routes should be bridged with control on both sides of the line
syat appropriate intervals. The standard symbol for indicating horizontal control on the
Engineering.netproject map is a triangle.
Horizontal control station
Project point
FIGURE 6.6 Station location 1.
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Static Global Positioning System Surveying 199
Vertical Control
Those stations with a published accuracy high enough for consideration as vertical
control are symbolized by an open square or circle on the map. Those stations that
are sufficient for both horizontal and vertical control are particularly helpful and are
designated by a combination of the triangle and square.
A minimum of four vertical control stations are needed to anchor a GPS static net-
work. A large project should have more. In general, the more benchmarks available, the
better. Vertical control is best located at the four corners of a project (see Figure 6.7).
Orthometric elevations are best transferred by means of classic spirit leveling;
such work should be built into the project plan when it is necessary. When spirit lev-
els are planned to provide vertical control positions, special care may be necessary to
ensure that the precision of such conventional work is as consistent as possible with
the rest of the survey. Route surveys require vertical control at the beginning and the
end. They should be bridged with benchmarks on both sides of the line at intervals
from 5 to 10 km.
wWhen the distances involved are too long for spirit leveling to be used effectively,
wtwo independent GPS measurements may suffice to connect a benchmark to the proj-
wect. However, it is important to recall the difference between the ellipsoidal heights
.Eavailable from a GPS observation and the orthometric elevations yielded by a level
asyEngineering.netcircuit.
Horizontal control station
Vertical control station
Project point
FIGURE 6.7 Station location 2.
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200 GPS for Land Surveyors
PREPARATION
Plotting Project Points
A solid dot is the standard symbol used to indicate the position of project points.
Some variation is used when a distinction must be drawn between those points that
are in place and those that must be set (see Figure 6.8).
When its location is appropriate, it is always a good idea to have a vertical or
horizontal control station serve double duty as a project point. While the precision of
their plotting may vary, it is important that project points be located as precisely as
possible even at this preliminary stage.
12
ww150w1.42Ea7sy9Engin6 ee8 r11ing3 .net
13 14
North
Scale: 1 in = 2 km
Horizontal control station
Vertical control station
Project point
FIGURE 6.8 Control and project points.
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Static Global Positioning System Surveying 201
The subsequent observation schedule will depend to some degree on the arrange-
ment of the baselines. Also, the preliminary evaluation of access, obstructions,
and other information depends on the position of the project point relative to these
features.
Evaluating Access
When all potential control and project positions have been plotted and given a unique
identifier, some aspects of the survey can be addressed a bit more specifically. If
good roads are favorably located, if open areas are indicated around the stations, and
if no station falls in an area where special permission will be required for its occu-
pation, then the preliminary plan of the survey ought to be remarkably trouble-free.
However, it is likely that one or more of these conditions will not be so fortunately
arranged.
The speed and efficiency of transportation from station to station can be assessed
to some degree from the project map. It is also wise to remember that while inclem-
went weather does not disturb GPS observations whatsoever, without sufficient prepa-
wration, it can play havoc with surveyors’ ability to reach points over difficult roads
wor by aircraft.
.EPlanning Offsets
aIf control stations or project points are located in areas where the map indicates that
sytopography or vegetation will obstruct the satellite’s signals, alternatives may be
Econsidered. A shift of the position of a project point into a clear area may be pos-
nsible where the change does not have a significant effect on the overall network. A
gicontrol station may also be the basis for a less obstructed position, transferred with a
neshort level circuit or traverse. Of course, such a transfer requires availability of con-
eventional surveying equipment on the project. In situations where such movement is
rinot possible, careful consideration of the actual paths of the satellites at the station
ngitself during on-site reconnaissance may reveal enough windows in the gaps between
.obstructions to collect sufficient data by strictly defining the observation sessions.
netPlanning Azimuth Marks
Azimuth marks are a common requirement in GPS projects. They are an accom-
paniment to static GPS stations when a client intends to use them to control sub-
sequent conventional surveying work. Of course, the line between the station and
the azimuth mark should be as long as convenience and the preservation of line of
sight allows.
It is wise to take care that short baselines do not degrade the overall integrity of
the project. Occupations of the station and its azimuth mark should be simultaneous
for a direct measurement of the baseline between them. Both should also be tied to
the larger network as independent stations. There should be two or more occupations
of each station when the distance between them is less than 2 km.
While an alternative approach may be to derive the azimuth between a GPS sta-
tion and its azimuth mark with an astronomic observation, it is important to remem-
ber that a small error, attributable to the deflection of the vertical, will be present in
such an observation. The small angle between the plumb line and a normal to the
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202 GPS for Land Surveyors
ellipsoid at the station can either be ignored, because they are likely to be quite simi-
lar at both ends, or removed with a Laplace correction.
Obtaining Permissions
Another aspect of access can be considered when the project map finally shows all
the pertinent points. Nothing can bring a well-planned survey to a halt faster than a
locked gate, an irate landowner, or a government official who is convinced he should
have been consulted previously. To the extent that it is possible from the available
mapping, affected private landowners and government jurisdictions should be identi-
fied and contacted. Taking this precaution at the earliest stage of the survey planning
can increase the chance that the sometimes long process of obtaining permissions,
gate keys, badges, or other credentials has a better chance of completion before the
survey begins.
On the other hand, any aspect of a GPS survey plan derived from examining map-
ping, virtual or hard copy, must be considered preliminary. Most features change
wwith time, and even those that are relatively constant cannot be portrayed on a map
wwith complete exactitude. Nevertheless, steps toward a coherent workable design can
wbe taken using the information they provide.
.EaSOME GPS SURVEY DESIGN FACTS
syThough much of the preliminary work in producing the plan of a GPS survey is
Ea matter of estimation, some hard facts must be considered, too. For example, the
nnumber of GPS receivers available for the work and the number of satellites above
githe observer’s horizon at a given time in a given place are two ingredients that can be
nedetermined with some certainty.
erinSoftware Assistance
g.Most GPS software packages provide users with routines that help them determine
nethe satellite windows, i.e., the periods of time when the largest numbers of satellites
tare simultaneously available. Today, observers are virtually assured of 24 hour cov-
erage; however, the mere presence of adequate satellites above an observer’s horizon
does not guarantee collection of sufficient data. Therefore, despite the virtual cer-
tainty that at least four satellites will be available, evaluation of their configuration
as expressed in the position dilution of precision (PDOP) is still crucial in planning
a GPS survey.
Position Dilution of Precision
The assessment of the productivity of a GPS survey almost always hinges, in part at
least, on the length of the observation sessions required to satisfy the survey specifi-
cations. The determination of the session’s duration depends on several particulars,
such as the length of the baseline and the relative position, i.e., the geometry, of the
satellites, among others.
Generally speaking, the larger the constellation of satellites, the better the avail-
able geometry, the lower the PDOP and the shorter the length of the session needed
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Static Global Positioning System Surveying 203
to achieve the required accuracy. For example, given six satellites and good geom-
etry, baselines of 10 km or less might require a session of 45 min to 1 hour, whereas,
under exactly the same conditions, a baseline over 20 km might require a session of
2 hours or more. Alternatively, 45 min of six-satellite data may be worth an hour of
four-satellite data, depending on the arrangement of the satellites in the sky.
Stated another way, the GPS receiver’s position is derived from the simultaneous
solution of vectors between it and the constellation of satellites above the observer’s
horizon. The quality of that solution depends, in large part, on the distribution of
those vectors. For example, any position determined when the satellites are crowded
together in one part of the sky will be unreliable, because all the vectors will have
virtually the same direction. Fortunately, a computer can predict such an unfavorable
configuration if it is given the ephemeris of each satellite, the approximate position
of the receiver, and the time of the planned observation. Provided with a forecast of
a large PDOP, the GPS survey planner should consider an alternate observation plan.
When one satellite is directly above the receiver and three others are near the
whorizon and 120° in azimuth from one another, the arrangement is nearly ideal for
wa four-satellite constellation. The planner of the survey would be likely to consider
wsuch a window. However, more satellites would improve the resulting position even
more, as long as they are well distributed in the sky above the receiver. In general,
.Ethe more satellites, the better. For example, if the planner finds eight satellites will be
aabove the horizon in the region where the work is to be done and the PDOP is below
sytwo, that window would be a likely candidate for observation.
EThere are other important considerations. The satellites are constantly moving in
nrelation to the receiver and to each other. Because satellites rise and set, the PDOP is
giconstantly changing. Within all this movement, the GPS survey designer must have
nesome way of correlating the longest and most important baselines with the longest
ewindows, the most satellites, and the lowest PDOP. Most GPS software packages,
rigiven a particular location and period of time, can provide illustrations of the satel-
nglite configuration.
.nePolar Plot
tOne such diagram is a plot of the satellite’s tracks drawn on a graphical representa-
tion of the upper half of the celestial sphere with the observer’s zenith at the center
and perimeter circle as the horizon. The azimuths and elevations of the satellites
above the specified mask angle are connected into arcs that represent the paths of all
available satellites. The utility of this sort of drawing has lessened with the comple-
tion of the GPS constellation. In fact, there are so many satellites available that the
picture can become quite crowded and difficult to decipher.
Another printout is a tabular list of the elevation and azimuth of each satellite at
time intervals selected by the user.
An Example
The position of point Morant in Table 6.2 needed expression to the nearest minute
only, a sufficient approximation for the purpose. The ephemeris data were 5 days
old when the chart was generated by the computer, but the data were still an ade-
quate representation of the satellite’s movements to use in planning. The mask angle
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204 GPS for Land SurveyorsSatellite Azimuth and Elevation Table 1
www.EasyEngineering.netPoint: MorantLat 36:45:0 N Lon 121:45:0 W Ephemeris 9/24/2014
Zone: Time Pacific Day (–7)
Downloaded From : www.EasyEngineering.netDate: Wed., Sept. 29, 2014Mask Angle: 15 (deg)
24 Satellites: 1 2 3 7 9 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31
Sampling Rate: 10 minutes
Time El Az El Az El Az El Az El Az El Az El Az El Az PDOP
Constellation of 8 SV’s 109 1.7
SV 2 16 18 19 27 28 29 31 104 1.8
99 1.8
0:00 16 219 15 317 77 121 66 330 41 287 23 65 36 129 30 93 1.9
88 1.8
0:10 20 221 18 314 73 131 67 641 44 292 22 60 32 132 33 82 1.8
0:20 24 23 20 310 68 137 68 353 47 297 21 56 28 135 35 3.0
3.0
0:30 28 226 22 306 64 142 68 5 50 302 20 51 24 138 36 2.8
2.6
0:40 32 229 23 302 59 146 67 17 52 308 18 48 20 140 37 (Continued)
0:50 36 232 24 297 54 148 66 28 55 314 16 44 16 142 38
Constellation of 6 SV’s
SV 2 16 18 19 27 31
1:00 40 235 24 293 49 151 65 39 58 320 38 76
1:10 43 239 24 288 44 153 63 49 61 328 37 70
1:20 47 244 24 283 40 155 61 57 634 336 36 64
1:30 51 249 23 278 35 156 59 65 66 345 34 60
TABLE 6.2 (CONTINUED) www.EasyEngineering.net Downloaded From : www.EasyEngineering.net
Satellite Azimuth and Elevation Table 1 Static Global Positioning System Surveying
Point: Morant Lat 36:45:0 N Lon 121:45:0 W Ephemeris 9/24/2014
Zone: Time Pacific Day (–7)
Date: Wed., Sept. 29, 2014 Mask Angle: 15 (deg)
24 Satellites: 1 2 3 7 9 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31
Sampling Rate: 10 minutes
Downloaded From : www.EasyEngineering.net Time El Az El Az El Az El Az El Az El Az El Az El Az PDOP
SV 2 Constellation of 7 SV’s
7 16 18 19 27 31
1:40 54 254 16 186 22 273 30 157 56 73 68 356 32 55 2.3
2.2
1:50 57 260 21 186 20 269 26 158 53 79 70 9 29 51 2.0
2:00 60 268 25 186 19 264 22 159 50 85 71 23 26 48
SV 2 Constellation of 8 SV’s
7 16 18 19 26 27 31
2:10 66 276 30 185 16 260 17 160 47 91 15 319 71 38 23 45 1.7
205
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206 GPS for Land Surveyors
was specified at 15°, so the program would consider a satellite set when it moved
below that elevation angle. The zone time was Pacific Daylight Time, 7 hours behind
Coordinated Universal Time. The full constellation provided 24 healthy satellites,
and the sampling rate indicated that the azimuth and elevation of those above the
mask angle would be shown every 10 min.
At 0:00 hour, satellite pseudorandom noise (PRN) 2 could be found on an azi-
muth of 219° and an elevation of 16° above the horizon by an observer at 36°45′Nφ
and 121°45′Wλ. Table 6.2 indicates that PRN 2 was rising and got continually
higher in the sky for the 2 hours and 10 min covered by the chart. The satellite
PRN 16 was also rising at 0:00 but reached its maximum altitude at about 1:10 and
began to set. Unlike PRN 2, PRN 16 was not tabulated in the same row throughout
the chart. It was supplanted when PRN 7 rose above the mask angle and PRN 16
shifted one column to the right. The same may be said of PRN 18 and PRN 19.
Both of these satellites began high in the sky, unlike PRN 28 and PRN 29. They
were just above 15° and setting when the table began and set after approximately
w1 hour of availability. They would not have been seen again at this location for about
w12 hours.
wThis chart indicated changes in the available constellation from eight space vehi-
cles, between 0:00 and 0:50, six between 1:00 and 1:30, seven from 1:40 to 2:00, and
.Eback to eight at 2:10. The constellation never dipped below the minimum of four
asatellites, and the PDOP was good throughout. The PDOP varied between a low of
sy1.7 and a high of 3.0. Over the interval covered by the table, the PDOP never reached
Ethe unsatisfactory level of 5 or 6, which is when a planner should avoid observation.
ngiChoosing the Window
neUsing this chart, the GPS survey designer might well have concluded that the best
eavailable window was the first. There was nearly an hour of eight-satellite data with
ria PDOP below 2. However, the data indicated that good observations could be made
ngat any time covered here, except for one thing: it was the middle of the night.
.nIonospheric Delay
etIt is worth noting that the ionospheric error is usually smaller after sundown. In
fact, the FGDC specified dual-frequency receivers for daylight observations for the
achievement of the highest accuracies, due, in part, to the increased ionospheric delay
during those hours.
Table 6.3 shows data from later in the day. It covers a period of two hours when
a constellation of five and six satellites was always available. However, through the
first hour, from 6:30 to 7:30, the PDOP hovered around 5 and 6. For the first half
of that hour, four of the satellites (PRN 9, PRN 12, PRN 13, and PRN 24) were all
near the same elevation. During the same period, PRN 9 and PRN 12 were only
approximately 50° apart in azimuth, as well. Even though a sufficient constellation
of satellites was constantly available, the survey designer may well have consid-
ered only the last 30 to 50 min of the time covered by this chart as suitable for
observation.
There is one caution, however. Azimuth-elevation tables are a convenient tool in
the division of the observing day into sessions, but it should not be taken for granted
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TABLE 6.3 www.EasyEngineering.net Downloaded From : www.EasyEngineering.net
Satellite Azimuth and Elevation Table 2 Static Global Positioning System Surveying
Point: Morant Lat 36:45:0 N Lon 121:45:0 W Ephemeris 9/24/2014
Zone: Time Pacific Day (–7)
Date: Wed., Sept. 29, 2014 Mask Angle: 15 (deg)
24 Satellites: 1 2 3 7 9 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31
Sampling Rate: 10 minutes
Time El Az El Az El Az El Az El Az El Az El Az El Az PDOP
Constellation of 5 SV’s
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6:30 28 54 60 271 61 319 62 15 48 177 6.3
6.0
6:40 24 57 60 261 66 314 57 19 53 176 5.3
4.6
6:50 21 60 59 252 70 305 53 22 58 175
7:00 18 62 57 243 73 292 49 25 63 172
Constellation of 5 SV’s 4.8
SV 9 12 13 20 24 5.7
7:10 54 235 74 274 44 28 16 308 68 169 5.1
7:20 51 229 74 255 40 32 20 310 72 163 4.0
7:30 47 224 72 238 37 35 23 311 77 153 (Continued)
7:40 43 219 68 226 33 38 27 313 80 134
207
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208 GPS for Land SurveyorsSatellite Azimuth and Elevation Table 2
www.EasyEngineering.netPoint: MorantLat 36:45:0 N Lon 121:45:0 W Ephemeris 9/24/2014
Zone: Time Pacific Day (–7)
Downloaded From : www.EasyEngineering.netDate: Wed., Sept. 29, 2014Mask Angle: 15 (deg)
24 Satellites: 1 2 3 7 9 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 31
Sampling Rate: 10 minutes
Time El Az El Az El Az El Az El Az El Az El Az El Az PDOP
Constellation of 6 SV’s 2.1
SV 9 12 13 16 20 24 2.3
7:50 39 215 64 218 29 41 16 149 31 314 81 102 2.4
8:00 35 212 59 213 26 45 19 146 36 314 80 73 2.5
8:10 31 209 54 209 23 48 23 143 40 315 76 57 2.5
8:20 27 207 49 206 19 52 27 140 44 314 72 49
8:30 23 204 44 204 16 55 30 137 48 314 67 45
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Static Global Positioning System Surveying 209
that every satellite listed is healthy and in service. For the actual availability of sat-
ellites and an update on atmospheric conditions, it is always wise to check the U.S.
Coast Guard’s website (http://www.navcen.uscg.gov/?Do=constellationstatus) before
and after a project. In the planning stage, the diligence can prevent creation of a
design dependent on satellites that prove unavailable. Similarly, after the field work
is completed, it can prevent inclusion of unhealthy data in the post-processing.
Supposing that the period from 7:40 to 8:30 was found to be a good window, the
planner may have regarded it as a single 50 min session, or divided it into shorter
sessions. One aspect of that decision was probably the length of the baseline in ques-
tion. In static GPS, a long line of 30 km may require 50 min of six-satellite data, but
a short line of 3 km may not. Another consideration was probably the approximation
of the time necessary to move from one station to another.
Naming the Variables
The next step in the static GPS survey design is drawing the preliminary plan of the
wbaselines on the project map. Once some idea of the configuration of the baselines
whas been established, an observation schedule can be organized. Toward that end, the
wFGCC developed a set of formulas, which will be used here.
For illustration, suppose that the project map (Figure 6.9) includes horizontal con-
.Etrol, vertical control, and project points for a planned GPS network. They will be
asymbolized by m. There are four multifrequency GPS receivers available for this
syproject. They will be symbolized by r. There will be five observation sessions each
Eday during the project. They will be symbolized by d. To summarize,
ngi m = total number of stations (existing and new) = 14
nee d = number of possible observing sessions per observing day = 5
ring r = number of receivers = 4 dual frequency
.neThe design developed from this map must be preliminary. The session for each
tday of observation will depend on the success of the work the day before. Please
recall that the plan must be provisional until the baseline lengths, the obstructions
at the observation sites, the transportation difficulties, the ionospheric disturbances,
and the satellite geometry are actually known. Those questions can only be answered
during the reconnaissance and the observations that follow. Even though these equiv-
ocations apply, the next step is to draw the baseline’s measurement plan.
Compatible Receivers
Relative static positioning, just as all the subsequent surveying methods discussed
here, involves several receivers occupying many sites. Problems can be avoided
as long as the receivers on a project are compatible. For example, it is helpful if
they have the same number of channels and signal processing techniques, and the
Receiver Independent Exchange (RINEX) format, developed by the Astronomical
Institute, allows different receivers and post-processing software to work together.
Almost all GPS processing software will output RINEX files.
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210 GPS for Land Surveyors
1 2
6
3
4
5
7
8
w 10 9
ww12
.Eas13 11
yEngineSession 14 North
e49-1
Receivers Scale: 1 in = 2 km
ABCD
1 3 8 13
ring.netSessionIndependent lines Trivial lines
1-3 3-8 8-13 13-1 1-8 3-13
Receivers Independent lines Trivial lines
ABCD
FIGURE 6.9 Drawing the baselines.
Receiver Capabilities and Baseline Length
The number and type of channels available to a receiver are considerations because,
generally speaking, the more satellites the receiver can track continuously, the better.
Another factor that ought to be weighed is whether a receiver has single or multi-
frequency capability. Single-frequency receivers are best applied to relatively short
baselines, say, under 25 km. The biases at one end of such a vector are likely to be
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Static Global Positioning System Surveying 211
similar to those at the other. Multifrequency receivers, however, have the capabil-
ity to nearly eliminate the effects of ionospheric refraction and can handle longer
baselines.
DRAWING THE BASELINES
Horizontal Control
A good rule of thumb is to verify the integrity of the horizontal control by observ-
ing baselines between these stations first. Vectors can be used to both corroborate
the accuracy of the published coordinates and later to resolve the scale, shift, and
rotation parameters between the control positions and the new network that will be
determined by GPS.
These baselines are frequently the longest in the project, and there is an added
benefit to measuring them first. By processing a portion of the data collected on the
longest baselines early in the project, the most appropriate length of the subsequent
wsessions can be found.
wThis test may allow improvement in the productivity on the job without erosion
wof the final positions.
.EaJulian Day in Naming Sessions
syThe table at the bottom of Figure 6.9 indicates that the name of the first session con-
Enecting the horizontal control is 49-1. The date of the planned session is given in the
nJulian system. Taken most literally, Julian dates are counted from January 1, 4713
gB.C. However, most practitioners of GPS use the term to mean the day of the current
inyear measured consecutively from January 1.
eeUnder this construction, because there are 31 days in January, Julian day 49 is
rFebruary 18 of the current year. The designation 49-1 means that this is to be the
infirst session on that day. Some prefer to use letters to distinguish the session. In that
gcase, the label would be 49-A.
.netIndependent Lines
This project will be done with four receivers. The table shows that receiver A will
occupy point 1; receiver B, point 3; receiver C, point 8; and receiver D, point 13 in the
first session. However, the illustration shows only three of the possible six base lines
that will be produced by this arrangement. Only the independent, also known as
nontrivial, lines are shown on the map. The three lines that are not drawn are called
trivial, and are also known as dependent lines. This idea is based on restricting the
use of the lines created in each observing session to the absolute minimum needed
to produce a unique solution.
Whenever four receivers are used, six lines are created. However, any three of
those lines will fully define the position of each occupied station in relation to the
others in the session.
Therefore, the user can consider any three of the six lines independent, but once
the decision is made, only those three baselines are included in the network. The
remaining baselines are then considered trivial and discarded. In practice, the three
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212 GPS for Land Surveyors
shortest lines in a four-receiver session are almost always deemed the independent
vectors, and the three longest lines are eliminated as trivial or dependent. That is the
case with the session illustrated.
Where r is the number of receivers, every session yields r − 1 independent base-
lines. For example, four receivers used in 10 sessions would produce 30 independent
baselines. It cannot be said that the shortest lines are always chosen to be the inde-
pendent lines. Sometimes there are reasons to reject one of the shorter vectors owing
to incomplete data, cycle slips, multipath, or some other weakness in the measure-
ments. Before such decisions can be made, each session will require analysis after
the data have actually been collected. In the planning stage, it is best to consider the
shortest vectors as the independent lines.
Another aspect of the distinction between independent and trivial lines involves
the concept of error of closure or loop closure. Loop closure is a procedure by which
the internal consistency of a GPS network is discovered. A series of baseline vec-
tor components from more than one GPS session, forming a loop or closed figure, is
wadded together. The closure error is the ratio of the length of the line representing the
wcombined errors of all the vector’s components to the length of the perimeter of the
wfigure. Any loop closures that only use baselines derived from a single common GPS
session will yield an apparent error of zero, because they are derived from the same
.Esimultaneous observations. For example, all the baselines between the four receiv-
aers in session 49-1 of the illustrated project will be based on ranges to the same GPS
sysatellites over the same period of time. Therefore, the trivial lines of 13-1, 1-8, and
E3-13 will be derived from the same information used to determine the independent
nlines of 1-3, 3-8, and 8-13. It follows that, if the fourth line from station 13 to station 1
giwere included to close the figure of the illustrated session, the error of closure would
nebe zero. The same may be said of the inclusion of any of the trivial lines. Their addi-
etion cannot add any redundancy or any geometric strength to the lines of the session
ribecause they are all derived from the same data. If redundancy cannot be added to a
ngGPS session by including any more than the minimum number of independent lines,
.how can the baselines be checked? Where does redundancy in GPS work come from?
netRedundancy
If only two receivers were used to complete the illustrated project, there would be no
trivial lines and it might seem there would be no redundancy at all. However, to con-
nect every station with its closest neighbor, each station would have to be occupied
at least twice, and each time during a different session. For example, with receiver A
on station 1 and receiver B on station 2, the first session could establish the base-
line between them. The second session could then be used to measure the base-
line between station 1 and station 4. It would certainly be possible to simply move
receiver B to station 4 and leave receiver A undisturbed on station 1. However, some
redundancy could be added to the work if receiver A were reset. If it were recentered,
replumbed, and its heights of measurement (H.I.) remeasured, some check on both
of its occupations on station 1 would be possible when the network was completed.
Under this scheme, a loop closure at the end of the project would have some meaning.
If one were to use such a scheme on the illustrated project and connect into one
loop all of the 14 baselines determined by the 14 two-receiver sessions, the resulting
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Static Global Positioning System Surveying 213
error of closure would be useful. It could be used to detect blunders in the work, such
as mis-measured heights of instruments. Such a loop would include many different
sessions. The ranges between the satellites and the receivers defining the baselines
in such a circuit would be from different constellations at different times. However,
if it were possible to occupy all 14 stations in the illustrated project with 14 differ-
ent receivers simultaneously and do the entire survey in one session, a loop closure
would be absolutely meaningless.
In the real world, such a project is not done with 14 receivers nor with 2 receivers,
but with 3, 4, or 5. The achievement of redundancy takes a middle road. The number
of independent occupations is still an important source of redundancy. In the two-
receiver arrangement every line can be independent, but that is not the case when a
project is done with any larger number of receivers. As soon as three or more receiv-
ers are considered, the discussion of redundant measurement must be restricted to
independent baselines, excluding trivial lines.
Redundancy is then partly defined by the number of independent baselines that
ware measured more than once, as well as by the percentage of stations that are occu-
wpied more than once. While it is not possible to repeat a baseline without reoccupy-
wing its endpoints, it is possible to reoccupy a large percentage of the stations in a
project without repeating a single baseline. These two aspects of redundancy in GPS
.E(i.e., the repetition of independent baselines and the reoccupation of stations) are
asomewhat separate.
syFigure 6.10 shows one of the many possible approaches to setting up the baselines
Efor this particular GPS project. The survey design calls for the horizontal control to
nbe occupied in session 49-1. It is to be followed by measurements between two con-
gitrol stations and the nearest adjacent project points in session 49-2. As shown in the
netable at the bottom of Figure 6.10, there will be redundant occupations on stations 1
eand 3. Even though the same receivers will occupy those points, their operators will
ribe instructed to reset them at different H.I.’s for the new session. A better, but prob-
ngably less efficient, plan would be to occupy these stations with different receivers
.than were used in the first session.
netForming Loops
As the baselines are drawn on the project map for a static GPS survey, or any GPS
work where accuracy is the primary consideration, the designer should remember
that part of their effectiveness depends on the formation of complete geometric fig-
ures. When the project is completed, these independent vectors should be capable
of formation into closed loops that incorporate baselines from two to four different
sessions. In the illustrated baseline plan, no loop contains more than ten vectors, no
loop is more than 100 km long, and every observed baseline will have a place in a
closed loop.
Finding the Number of Sessions
The illustrated survey design calls for 10 sessions, but the calculation does not
include human error, equipment breakdown, and other unforeseeable difficulties. It
would be impractical to presume a completely trouble-free project. The FGCC pro-
posed the following formula for arriving at a more realistic estimate:
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214 GPS for Land Surveyors
s = (m ⋅ n) + (m ⋅ n)( p − 1) + k ⋅m
r r
where
s = number of observing sessions
r = number of receivers
m = total number of stations involved
12
3
4
w5 6
w7
w.EasyEngin10 8
eerin12 9
11
g.net13 14 North
Session Receivers Independent lines Trivial lines Scale: 1 in = 2 km
ABCD
49-1 1-3 3-8 8-13 13-1 1-8 3-13
49-2 1 3 8 13 1-2 2-3 1-4 1-3 3-4 2-4
49-3 1324 5-4 4-2 2-6 5-6 2-5 4-6
49-4 5 62 4 5-7 7-9 6-7 5-6 6-9 5-9
49-5 5 67 9 1-5 5-10 10-13
5 1 10 13 1-10 1-13 5-13
Session Receivers Independent lines Trivial lines
ABCD
50-1 10 12 7 9 7-10 10-12 9-12 7-12 9-10 7-9
50-2 9-12 12-13 9-14 13-14 12-14 9-13
50-3 14 12 13 9 13-14 14-11 11-8 13-8 8-14 13-11
50-4 14 8 13 11 9-11 8-14 14-11
50-5 14 8 11 9 14-9 8-9 8-11
7 63 8 6-8 6-7 3-6 3-8 3-7 7-8
FIGURE 6.10 Drawing the baselines.
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Static Global Positioning System Surveying 215
The values n, p, and k require a bit more explanation. The variable n is a represen-
tation of the level of redundancy that has been built into the network, based on the
number of occupations on each station. The illustrated survey design includes more
than two occupations on all but 4 of the 14 stations in the network. In fact, 10 of the
14 positions will be visited three or four times in the course of the survey. There are
a total of 40 occupations by the four receivers in the 10 planned sessions. By divid-
ing 40 occupations by 14 stations, it can be found that each station will be visited an
average of 2.857 times. Therefore, the planned redundancy represented by factor n is
equal to 2.857 in this project.
The experience of a firm is symbolized by the variable p in the formula. The divi-
sion of the final number of actual sessions required to complete past projects by the
initial estimation yields a ratio that can be used to improve future predictions. That
ratio is the production factor p. A typical production factor is 1.1.
A safety factor of 0.1, known as k, is recommended for GPS projects within 100 km
of a company’s home base. Beyond that radius, an increase to 0.2 is advised.
wThe substitution of the appropriate quantities for the illustrated project increases
wthe prediction of the number of observation sessions required for its completion:
w.Eas
(m ⋅ n) (m ⋅ n)( p − 1)
r r
syEs= + + k ⋅m
(14)(2.857) (14)(2.857)(1.1− 1)
4 4
ngi = + + (0.2)(14)
nes = 10 +1+ 2.8s=(40)+(4) + 2.8
4 4
eris = 14 sessions (rounded to the nearest integer)
ng.In other words, the 2-day, 10-session schedule is a minimum period for the base-
neline plan drawn on the project map. A more realistic estimate of the observation
tschedule includes 14 sessions. It is also important to keep in mind that the observa-
tion schedule does not include time for on-site reconnaissance.
Ties to the Vertical Control
The ties from the vertical control stations to the overall network are usually not
handled by the same methods used with the horizontal control. The first session of
the illustrated project was devoted to occupation of all the horizontal control sta-
tions. There is no similar method with the vertical control stations. First, the geoidal
undulation would be indistinguishable from baseline measurement error. Second,
the primary objective in vertical control is for each station to be adequately tied to its
closest neighbor in the network.
If a benchmark can serve as a project point, it is nearly always advisable to use it,
as was done with stations 11 and 14 in the illustrated project. A conventional level
circuit can often be used to transfer a reliable orthometric elevation from vertical
control station to a nearby project point.
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216 GPS for Land Surveyors
STATIC GPS CONTROL OBSERVATIONS
The prospects for the success of a GPS project are directly proportional to the qual-
ity and training of the people doing it. The handling of the equipment, the on-site
reconnaissance, the creation of field logs, and the inevitable last-minute adjustments
to the survey design all depend on the training of the personnel involved for their
success. There are those who say the operation of GPS receivers no longer requires
highly qualified survey personnel. That might be true if effective GPS surveying
needed only the pushing of the appropriate buttons at the appropriate time. In fact,
when all goes as planned, it may appear to the uninitiated that GPS has made experi-
enced field surveyors obsolete. However, when the unavoidable breakdowns in plan-
ning or equipment occur, the capable people, who seemed so superfluous moments
before, suddenly become indispensable.
Equipment
wwConventional Equipment
wMost GPS projects require conventional surveying equipment for spirit-leveling cir-
cuits, offsetting horizontal control stations, and monumenting project points, among
.Eother things. It is perhaps a bit ironic that this most advanced surveying method also
afrequently has need of the most basic equipment. The use of brush hooks, machetes,
syaxes, and so forth, can sometimes salvage an otherwise unusable position by remov-
Eing overhead obstacles. Another strategy for overcoming such hindrances has been
ndeveloped using various types of survey masts to elevate a separate GPS antenna
giabove the obstructing canopy.
neFlagging, paint, and the various techniques of marking that surveyors have
edeveloped over the years are still a necessity in GPS work. The pressure of work-
riing in unfamiliar terrain is often combined with urgency. Even though there is
ngusually not a moment to spare in moving from station to station, a GPS surveyor
.frequently does not have the benefit of having visited the particular points before.
neIn such situations, the clear marking of both the route and the station during recon-
tnaissance is vital.
Despite the best route marking, a surveyor may not be able to reach the planned
station, or, has arrived, finds some new obstacle or unanticipated problem that can
only be solved by marking and occupying an impromptu offset position for a session.
A hammer, nails, shiners, paint, and so forth, are essential in such situations.
In short, the full range of conventional surveying equipment and expertise have a
place in GPS. For some, their role may be more abbreviated than it was formerly, but
one element that can never be outdated is good judgment.
Safety Equipment
The high-visibility vests, cones, lights, flagmen, and signs needed for traffic control
cannot be neglected in GPS work. Unlike conventional surveying operations, GPS
observations are not deterred by harsh weather. Occupying a control station in a
highway is dangerous enough under the best of conditions, but in the midst of a
rainstorm, fog, or blizzard, it can be absolute folly without the proper precautions.
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Static Global Positioning System Surveying 217
And any time and trouble taken to avoid infraction of the local regulations regarding
traffic management will be compensated by an uninterrupted observation schedule.
Weather conditions also affect travel between the stations of the survey, both in
vehicles and on foot. Equipment and plans to deal with emergencies should be part of
any GPS project. First aid kits, fire extinguishers, and the usual safety equipment are
necessary. Training in safety procedures can be an extraordinary benefit, but perhaps
the most important capability in an emergency is communication.
Communications
Whether the equipment is handheld or vehicle mounted, two-way radios and cell
phones are used in most GPS operations. However, the line of sight that is no longer
necessary for the surveying measurements in GPS is sorely missed in the effort to
maintain clear radio contact between the receiver operators. A radio link between
surveyors can increase the efficiency and safety of a GPS project, but it is particu-
larly valuable when last minute changes in the observation schedule are necessary.
wWhen an observer is unable to reach a station or a receiver suddenly becomes inoper-
wable, unless adjustments to the schedule can be made quickly, each end of all of the
wlines into the missed station will require re-observation.
The success of static GPS hinges on all receivers collecting their data simulta-
.Eneously. However, it is more and more difficult to ensure reliable communication
abetween receiver operators in geodetic surveys, especially as their lines grow longer.
syHigh-wattage, private-line FM radios are quite useful when line of sight is avail-
Eable between them or when a repeater is available. The use of cell phones may elimi-
nnate the communication problem in some areas but probably not in remote locations.
giDespite the limitations of the systems available at the moment, achievement of the
nebest possible communication between surveyors on a GPS project pays dividends in
ethe long run.
rinGPS Equipment
g.Most GPS receivers capable of geodetic accuracy are designed to be mounted on a
netripod, usually with a tribrach and adaptor. However, there is a trend toward bipod-
tor range-pole-mounted antennas. An advantage of these devices is that they ensure a
constant height of the antenna above the station. The mis-measured height of the
antenna above the mark is probably the most pervasive and frequent blunder in GPS
control surveying.
The tape or rod used to measure the height of the antenna is sometimes built into
the receiver and, sometimes a separate device. It is important that the H.I. be mea-
sured accurately and consistently in both feet and meters, without merely converting
from one to the other mathematically. It is also important that the value be recorded
in the field notes and, where possible, also entered into the receiver itself.
Where tribrachs are used to mount the antenna, the tribrach’s optical centering
should be checked and calibrated. It is critical that the effort to perform GPS surveys
to an accuracy of centimeters not be frustrated by inaccurate centering or H.I. mea-
surement. Because many systems measure the height of the antenna to the edge of
the ground plane or to the exterior of the receiver itself, the calibration of the tribrach
affects both the centering and the H.I. measurement. The resetting of a receiver that
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218 GPS for Land Surveyors
occupies the same station in consecutive sessions is an important source of redun-
dancy for many kinds of GPS networks. However, integrity can only be added if the
tribrach has been accurately calibrated.
The checking of the carrier phase receivers themselves is also critical to the con-
trol of errors in a GPS survey, especially when different receivers or different models
of antennas are to be used on the same work. The zero baseline test is a method that
may be used to fulfill equipment calibration specifications where a three-dimensional
test network of sufficient accuracy is not available. As a matter of fact, the simplicity
of this test is an advantage. It is not dependent on special software or a test network.
This test can also be used to separate receiver difficulties from antenna errors.
Two or more receivers are connected to one antenna with a signal or antenna
splitter. The antenna splitter can be purchased from specialty electronics shops and is
also available online. An observation is done with the divided signal from the single
antenna reaching both receivers simultaneously. Because the receivers are sharing
the same antenna, satellite clock biases, ephemeris errors, atmospheric biases, and
wmultipath are all canceled. In the absence of multipath, the only remaining errors are
wattributable to random noise and receiver biases. The success of this test depends on
wthe signal from one antenna reaching both receivers, but the current from only one
receiver can be allowed to power the antenna. This test checks not only the precision
.Eof the receiver measurements but also the processing software. The results of the test
ashould show a baseline of only a few millimeters. Information is also available on
syNational Geodetic Survey (NGS) calibration baselines throughout the United States.
EnAuxiliary Equipment
giTools to repair the ends of connecting cables, a simple pencil eraser to clean the con-
netacts of circuit boards, or any of a number of small implements have saved more than
eone GPS observation session from failure. Experience has shown that GPS surveying
rirequires at least as much resourcefulness, if not more, than conventional surveying.
ngThe health of the batteries is a constant concern in GPS. There is simply nothing to
.be done when a receiver’s battery is drained but to resume power as soon as possible.
neA backup power source is essential. Cables to connect a vehicle battery, an extra fully-
tcharged battery unit, or both should be immediately available to every receiver operator.
Information
The information every GPS observer carries throughout a project ought to include
emergency phone numbers; the names, addresses, and phone numbers of relevant prop-
erty owners; and the combinations to necessary locks. Each member of the team should
also have a copy of the project map, any other maps that are needed to clarify position or
access, and, perhaps most important of all, the updated observation schedule.
The observation schedule for static GPS work will be revised daily based on
actual production (see Table 6.4). It should specify the start-stop times and station
for all the personnel during each session of the upcoming day. In this way, the sched-
ule will not only serve to inform every receiver operator of his or her own expected
occupations, but those of every other member of the project as well. This knowledge
is most useful when a sudden revision requires observers to meet or replace one
another.
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TABLE 6.4 www.EasyEngineering.net Downloaded From : www.EasyEngineering.net
Observation Schedule Static Global Positioning System Surveying
Downloaded From : www.EasyEngineering.net Svs PRNs Session 1 8:10 Session 2 9:50 Session 3 11:15 Session 4 12:30 Session 5
Receiver A Start 7:10 to Start 8:40 to Start 10:15 to Start 11:30 to Start 14:00
Dan H. Stop 8:10 Stop 9:50 Stop 11:15 Stop 12:30 Stop 15:00
9,12,13, 8:40 3,12,13, 10:15 3,12,13,16, 11:30 3,16,17,20, 14:00 1,3,17,21,
Receiver B 16,20,24 Re-set 16,20,24 17,20,24 22,23,26 23,26,28
Scott G. Move Re-set Re-set
Station 1 Re-set Station 1 Station 5 Station 5 Station 5
Receiver C NGS horiz. NGS horiz. NGS benchmark NGS benchmark NGS benchmark
Dewey A. Move
control control Move Station 6 Re-set Station 6 Move Station 1
Receiver D Station 3 Move Station 3 Re-Set Project point Move Project point Move NGS horiz.
Cindy E. NGS V&H NGS V&H
control control Station 2 Station 7 control
Station 8 Station 2 Project point Project point Station 10
NGS horiz. Project point NGS benchmark
control
Station 13 Station 4 Re-Set Station 4 Move Station 9 Move Station 13
NGS horiz. Project point Project point Project point NGS horiz.
control
control
219
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220 GPS for Land Surveyors
Station Data Sheet
The principles of good field notes have a long tradition in land surveying, and they
will continue to have validity for some time to come. In GPS, the ensuing paper trail
will not only fill subsequent archives; it has immediate utility. For example, the sta-
tion data sheet is often an important bridge between on-site reconnaissance and the
actual occupation of a monument.
Though every organization develops its own unique system of handling its field
records, most have some form of the station data sheet. The document illustrated in
Figure 6.11 is merely one possible arrangement of the information needed to recover
the station.
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FIGURE 6.11 Station data sheet.
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Static Global Positioning System Surveying 221
The station data sheet can be prepared at any period of the project, but perhaps the
most usual times are during the reconnaissance of existing control or immediately
after the monumentation of a new project point.
Neatness and clarity, always paramount virtues of good field notes, are of par-
ticular interest when the station data sheet is to be later included in the final report
to the client. The overriding principle in drafting a station data sheet is to guide
succeeding visitors to the station without ambiguity. A GPS surveyor on the way to
observe the position for the first time may be the initial user of a station data sheet.
A poorly written document could void an entire session if the observer is unable to
locate the monument. A client, later struggling to find a particular monument with an
inadequate data sheet, may ultimately question the value of more than the field notes.
Station Name
The station name fills the first blank on the illustrated data sheet. Two names for
a single monument are far from unusual. In this case the vertical control station,
wofficially named S 198, is also serving as a project point, number 14, but two names
wpurporting to represent the same position can present a difficulty. For example, when
wa horizontal control station is remonumented, a number 2 is sometimes added to
the original name of the station and it can be confusing. For example, it can be
.Eeasy to mistake station “Thornton 2” with an original station named “Thornton”
athat no longer exists. Both stations may still have a place in the published record,
sybut with slightly different coordinates. Another unfortunate misunderstanding can
Eoccur when inexperienced field personnel mistake a reference mark for the actual
nstation itself. Taking rubbings and/or close-up photographs are widely recommended
gito avoid such blunders regarding stations names or authority.
neeRubbings
riThe illustrated station data sheet provides an area to accommodate a rubbing. With
ngthe paper held on top of the monument’s disk, a pencil is run over it in a zigzag pat-
.tern producing a positive image of the stamping. This method is a bit more awkward
nethan simply copying the information from the disk onto the data sheet, but it does
thave the advantage of ensuring the station was actually visited and that the stamping
was faithfully recorded. Such rubbings or close-up photographs are often required.
Photographs
The use of photographs is growing as a help for the perpetuation of monuments. It
can be convenient to photograph the area around the mark as well as the monument
itself. These exposures can be correlated with a sketch of the area. Such a sketch can
show the spot where the photographer stood and the directions toward which the pic-
tures were taken. The photographs can then provide valuable information in locating
monuments, even if they are later obscured. Still, the traditional ties to prominent
features in the area around the mark are the primary agent of their recovery.
Quad Sheet Name
Providing the name of the appropriate state, county, and USGS quad sheet helps to cor-
relate the station data sheet with the project map. The year the mark was monumented,
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222 GPS for Land Surveyors
the monument description, the station name, and the “to-reach” description all help
to associate the information with the correct official control data sheet and, most
importantly, the correct station coordinates.
To-Reach Descriptions
When driving or walking to a position can be aided by computerized turn-by-turn
navigation, it is a great tool that may make writing to-reach descriptions unneces-
sary. However, GPS control work is often done in areas where the roadway mapping
in such navigations aids is inadequate. In those situations, the description of the route
to the station is one of the most critical documents written during the reconnais-
sance. Even though it is difficult to prepare the information in unfamiliar territory
and although every situation is somewhat different, there are some guidelines to be
followed. It is best to begin with the general location of the station with respect to
easily found local features.
The description in Figure 6.11 relies on a road junction, guard station, and local
wbusiness. After defining the general location of the monument, the description should
wrecount directions for reaching the station. Starting from a prominent location, the
directions should adequately describe the roads and junctions. Where the route is
wdifficult or confusing, the reconnaissance team should not only describe the junc-
.Etions and turns needed to reach a station; it is wise to also mark them with lath and
aflagging, when possible. It is also a good idea to note gates. Even if they are open
syduring reconnaissance, they may be locked later. When turns are called for, it is best
Eto describe not only the direction of the turn, but the new course, too. For example,
nin the description in Figure 6.11 the turn onto the dim road from the Tee River Road
giis described to the “left (northwest).” Roads and highways should carry both local
nnames and designations found on standard highway maps. For example in Figure
ee6.11, Tee River Road is also described as State Highway 20.
riThe “to-reach” description should certainly state the mileages as well as the travel
ntimes where they are appropriate, particularly where packing-in is required. Land
g.ownership, especially if the owner’s consent is required for access, should be men-
netioned. The reconnaissance party should obtain the permission to enter private prop-
terty and should inform the GPS observer of any conditions of that entry. Alternate
routes should be described where they may become necessary. It is also best to make
special mention of any route that is likely to be difficult in inclement weather.
Where helicopter access is anticipated, information about the duration of flights
from point to point, the distance of landing sites from the station, and flight time to
fuel supplies should be included on the station data sheet.
Flagging and Describing the Monument
Flagging the station during reconnaissance may help the observer find the mark more
quickly. On the station data sheet, the detailed description of the location of the station
with respect to roads, fence lines, buildings, trees, and any other conspicuous features
should include measured distances and directions. A clear description of the monument
itself is important. It is wise to also show and describe any nearby marks, such as refer-
ence marks, that may be mistaken for the station or aid in its recovery. The name of the
preparer, a signature, and the date round out the initial documentation of a GPS station.
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Static Global Positioning System Surveying 223
Visibility Diagrams
Obstructions above the mask angle of a GPS receiver must be taken into account in
finalizing the observation schedule. A station that is blocked to some degree is not
necessarily unusable, but its inclusion in any particular session is probably contin-
gent on the position of the specific satellites involved.
An Example
The diagram in Figure 6.12 is widely used to record such obstructions during recon-
naissance. It is known as a station visibility diagram, a polar plot, or a skyplot. The
concentric circles are meant to indicate 10° increments along the upper half of the
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FIGURE 6.12 Station visibility diagram.
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224 GPS for Land Surveyors
celestial sphere, from the observer’s horizon at 0° on the perimeter, to the observer’s
zenith at 90° in the center. The hemisphere is cut by the observer’s meridian, shown
as a line from 0° in the north to 180° in the south.
The prime vertical is signified as the line from 90° in the east to 270° in the
west. The other numbers and solid lines radiating from the center, every 30°
around the perimeter, are azimuths from north and are augmented by dashed
lines every 10°.
Drawing Obstructions
Using a compass and a clinometer, a member of the reconnaissance team can fully
describe possible obstructions of the satellite’s signals on a visibility diagram. By
standing at the station mark and measuring the azimuth and vertical angle of points
outlining the obstruction, the observer can plot the object on the visibility diagram.
For example, a windmill base is shown in Figure 6.12 as a cross-hatched figure. It
has been drawn from the observer’s horizon up to 37° in vertical angle from 168°, to
wabout 182° in azimuth at its widest point. This description by approximate angular
wvalues is entirely adequate for determining when particular satellites may be blocked
wat this station.
For example, suppose a 1 hour session from 9:10 to 10:10, illustrated in Table 6.5,
.Ewas under consideration for the observation on station S 198. The station visibility
achart might motivate a careful look at space vehicle (SV) PRN 16. Twenty minutes
syinto the anticipated session, at 9:30 SV 16 has just risen above the 15° mask angle.
EUnder normal circumstances, it would be available at station S 198, but it appears
nfrom the polar plot that the windmill will block its signals from reaching the receiver.
giIn fact, the signals from SV 16 will apparently not reach station S 198 until sometime
neafter the end of the session at 10:10.
eriWorking around Obstructions
ngUnder the circumstances, some consideration might be given to observing station
.S 198 during a session when none of the satellites would be blocked. However, the
ne9:10 to 10:10 session may be adequate after all. Even if SV 16 is completely blocked,
tthe remaining five satellites will be unobstructed and the constellation still will have
a relatively low position dilution of precision (PDOP). Still, the analysis must be car-
ried to other stations that will be occupied during the same session. The success of
the measurement of any baseline depends on common observations at both ends of
the line. Therefore, if the signals from SV 16 are garbled or blocked from station S 198,
any information collected during the same session from that satellite at the other end
of a line that includes S 198 will be useless in processing the vector between those
two stations.
The material of the base of the abandoned windmill has been described on the
visibility diagram as cross-membered steel, so it is possible that the signal from
SV 16 will not be entirely obstructed during the whole session. There may actu-
ally be more concern of multipath interference from the structure than that of
signal availability. One strategy for handling the situation might be to program
the receiver at S 198 to ignore the signal from SV 16 completely if the particular
receiver allows it.
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TABLE 6.5www.EasyEngineering.net Downloaded From : www.EasyEngineering.net
Satellite Azimuth and Elevation Table 3 Static Global Positioning System Surveying
Time El Az El Az El Az El Az El Az El Az El Az El Az PDOP
SV 3 12 13 Constellation of 5 SV’s
20 24
8:50 54 235 74 274 44 28 16 308 68 169 4.8
5.7
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4.0
9:10 47 224 72 238 37 35 23 311 77 153
9:20 43 219 68 226 33 38 27 313 80 134
SV 3 12 13 Constellation of 6 SV’s 24
16 20
9:30 39 215 64 218 29 41 16 179 31 314 81 102 2.1
2.3
9:40 35 212 59 213 26 45 19 176 36 314 80 73 2.4
2.5
9:50 31 209 54 209 23 48 23 173 40 315 76 57 2.5
10:00 27 207 49 206 19 52 27 170 44 314 72 49
10:10 23 204 44 204 16 55 30 167 48 314 67 45
225
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226 GPS for Land Surveyors
The visibility diagram (Figure 6.12) and the azimuth-elevation table (Table 6.5)
complement each other. They provide the field supervisor with the data needed to
make informed judgments about the observation schedule. Even if the decision is
taken to include station S 198 in the 9:10 to 10:10 session as originally planned, the
supervisor will be forewarned that the blockage of SV 16 may introduce a bit of
weakness at that particular station.
Approximate Station Coordinates
The latitude and longitude given on the station visibility diagram should be under-
stood to be approximate. It is sometimes a scaled coordinate or it may be taken
from another source. In either case, its primary role is as input for the receiver at the
beginning of its observation. The coordinate need only be close enough to the actual
position of the receiver to minimize the time the receiver must take to lock onto the
constellation of satellites it expects to find.
wMultipath
wThe multipath condition is by no means unique to GPS. When a transmitted televi-
wsion signal reaches the receiving antenna by two or more paths, the resulting varia-
.tions in amplitude and phase cause the picture to have ghosts. This kind of scattering
Eof the signals can be caused by reflection from land, water, or man-made structures.
asIn GPS, the problem can be particularly troublesome when signals are received from
ysatellites at low elevation angles; hence, the general use of a 15° to 20° mask angle.
EThe use of choke ring antennas to mediate multipath may also be considered.
ngIt is also wise, where it is possible, to avoid using stations that are near structures
ilikely to be reflective or to scatter the signal. For example, chain-link fences that
neare found hard against a mark can cause multipath by forcing the satellite’s signal
eto pass through the mesh to reach the antenna. The elevation of the antenna over the
ritop of the fence with a survey mast is often the best way to work around this kind
ngof obstruction. Metal structures with large flat surfaces are notorious for causing
.multipath problems. A long train moving near a project point could be a potential
neproblem, but vehicles passing by on a highway or street usually are not, especially if
tthey go by at high speed. It is important, of course, to avoid parked vehicles. It is best
to remind new GPS observers that the survey vehicle should be parked far enough
from the point to avert any multipath. A good way to handle these unfavorable condi-
tions is to set an offset point.
Point Offsets
An offset must, of course, stand far enough away from the source of multipath or an
attenuated signal to be unaffected. However, the longer the distance from the origi-
nally desired position the more important the accuracy of the bearing and distance
between that position and the offset becomes. Recording the tie between the two
correctly is crucial to avoid misunderstanding after the work is completed. Some
receivers allow input of the information directly into the observations recorded in
the receiver or data logger. However, during a control survey, it is best to also record
the information in a field book.
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Static Global Positioning System Surveying
Obstructed
point
Azimuth
point
Azimuth
D
i
s
t
a
n
c
e
Static GPS point offset
wFIGURE 6.13 Static point offset.
ww.Offsets in GPS control surveying are an instance where conventional surveying
Eequipment and expertise are necessary. Clearly, the establishment of the tie requires
asa position for the occupation of the instrument (i.e., a total station) and a position for
ythe establishment of its orientation (i.e., an azimuth) (see Figure 6.13). It is best to
Enestablish three intervisible rather than two points, one to occupy and two azimuth
gmarks. This approach makes it possible to add a redundant check to the tie. The posi-
intions on these two, or three, points may be established by setting monuments and
eperforming static observations on them all. Alternatively, azimuthal control may be
eestablished by astronomic observations.
ringLook for Multipath
.nBoth the GPS field supervisor and the reconnaissance team should be alert to any
etindications on the station visibility diagram that multipath may be a concern. Before
the observations are done, there is nearly always a simple solution. Discovering mul-
tipath in the signals after the observations are done is not only frustrating but also
often expensive.
Monumentation
The monumentation set for GPS projects varies widely and can range from brass
tablets to aerial premarks, capped rebar, or even pin flags. The objective of most sta-
tion markers is to adequately serve the client’s subsequent use. However, the time,
trouble, and cost in most high-accuracy GPS work warrant the most permanent,
stable monumentation.
Many experts predict that GPS will eventually make monumentation unneces-
sary. The idea foresees GPS receivers in constant operation at well-known master
stations that will allow surveyors with receivers to determine highly accurate relative
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228 GPS for Land Surveyors
positions with such speed and ease that monumentation will be unnecessary. The
idea may prove prophetic, but for now, monumentation is an important part of most
GPS projects. The suitability of a particular type of monument is an area still most
often left to the professional judgment of the surveyors involved.
Logistics
Scheduling
Once all the station data sheets, visibility diagrams, and other field notes have been
collected, the schedule can be finalized for the first observations. There will almost
certainly be changes from the original plan. Some of the anticipated control stations
may be unavailable or obstructed. Some project points may be blocked, too difficult
to reach, or simply not serve the purpose as well as a control station at an alternate
location. When the final control has been chosen, the project points have been monu-
mented, and the reconnaissance has been completed, the information can be brought
wtogether with some degree of certainty that it represents the actual conditions in the
wfield.
wNow that the access and travel time, the length of vectors, and the actual obstruc-
.tions are more certainly known, the length and order of the sessions can be solidified.
EDespite all the care and planning that goes into preparing for a project, unexpected
aschanges in the satellites’ orbits or health can upset the best schedule at the last min-
yute. It is always helpful to have a backup plan.
EThe receiver operators usually have been involved in the reconnaissance and are
ngfamiliar with the area and many of the stations. Even though an observer may not
ihave visited the particular stations scheduled for him, the copies of the project map,
neappropriate station data sheets, and visibility diagrams will usually prove adequate
eto their location.
ringObservation
.neWhen everything goes as planned, a GPS observation is uneventful. However, even
tbefore the arrival of the receiver operator at the control or project point the session
can get off-track. The simultaneity of the data collected at each end of a baseline is
critical to the success of any measurement in static GPS control surveys. When a
receiver occupies a master station throughout a project, there need be little concern
on this subject, but most static applications depend on the sessions of many mobile
receivers beginning and ending together.
Arrival
The number of possible delays that may befall an observer on the way to a station are too
numerous to mention. With proper planning and reconnaissance, the observer will likely
find that there is enough time for the trip from station to station and that sufficient infor-
mation is on hand to guide him to the position, but this, too, cannot be guaranteed. When
the observer is late to the station, the best course is usually to set up the receiver quickly
and collect as much data as possible. The baselines into the late station may or may not
be saved, but they will certainly be lost if the receiver operator collects no information at
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Static Global Positioning System Surveying 229
all. It is at times like these that good communication between the members of the GPS
team is most useful. For example, some of the other observers in the session may be able
to stay on their station a bit longer with the late arrival and make up some of the lost data.
Along the same line, it is usually a good policy for those operators who are to remain on
a station for two consecutive sessions to collect data as long as possible, while still leav-
ing themselves enough time to reset between the two observation periods.
Setup
Centering an instrument over the station mark is always important. However, the
centimeter-level accuracy of static GPS gives the centering of the antenna special
significance. It is ironic that such a sophisticated system of surveying can be defeated
from such a commonplace procedure. A tribrach with an optical plummet or any
other device used for centering should be checked and, if necessary, adjusted before
the project begins. With good centering and leveling procedures, an antenna should
be within a few millimeters of the station mark.
wUnfortunately, the centering of the antenna over the station does not ensure that
wits phase center is properly oriented. The contours of equal phase around the anten-
wna’s electronic center are not themselves perfectly spherical. Part of their eccentric-
.ity can be attributed to unavoidable inaccuracies in the manufacturing process. To
Ecompensate for some of this offset, it is a good practice to rotate all antennas in a
assession to the same direction. Many manufacturers provide reference marks on their
yantennas so that each one may be oriented to the same azimuth. That way they are
Eexpected to maintain the same relative position between their physical and electronic
ngcenters when observations are made.
iThe antenna’s configuration also affects another measurement critical to success-
neful GPS surveying: the height of the instrument. The frequency of mistakes in this
eimportant measurement is remarkable. Several methods have been devised to focus
rispecial attention on the height of the antenna. Not only should it be measured in
ngboth feet and meters, it should also be measured immediately after the instrument is
.set up and just before tearing it down to detect any settling of the tripod during the
netobservation.
Height of Instrument
The measurement of the height of the antenna in a GPS survey is often not made on
a plumb line. A tape is frequently stretched from the top of the station monument to
some reference mark on the antenna or the receiver itself. Some GPS teams measure
and record the height of the antenna to more than one reference mark on the ground
plane. These measurements are usually mathematically corrected to plumb.
The care ascribed to the measurement of antenna heights is due to the same con-
cern applied to centering. GPS has an extraordinary capability to achieve accurate
heights, but those heights can be easily contaminated by incorrect H.I.s.
Observation Logs
Most GPS operations require its receiver operators to keep a careful log of each
observation. Usually written on a standard form, these field notes provide a written
record of the measurements, times, equipment, and other data that explains what
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230 GPS for Land Surveyors
actually occurred during the observation itself. It is difficult to overestimate the
importance of this information. It is usually incorporated into the final report of the
survey, the archives. However, the most immediate use of the observation log is in
evaluation of the day’s work by the on-site field supervisor.
An observation log may be organized in a number of ways. The log illustrated in
Figure 6.14 is one method that includes some of the information that might be used
to document one session at one station.
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FIGURE 6.14 Observation log.
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Static Global Positioning System Surveying 231
Of course, the name of the observer and the station must be included, and while
the date need not be expressed in both the Julian and Gregorian calendars that infor-
mation may help in quick cataloging of the data. The approximate latitude, longi-
tude, and height of the station are usually required by the receiver as a reference
position for its search for satellites. The date of the planned session will not neces-
sarily coincide with the actual session observed. The observer’s arrival at the point
may have been late or the receiver may have been allowed to collect data beyond the
scheduled end of the session.
There are various methods used to name observation sessions in terminology that is
sensible to computers. A widely used system is noted here. The first four digits are the
project point’s number. In this case it is point 14 and is designated 0014. The next three
digits are the Julian day of the session; in this case it is day 50, or 050. Finally, the session
illustrated is the second of the day, or 2. Therefore, the full session name is 0014 050 2.
Whether onboard or separate, the type of antenna used and the height of the
antenna are critical pieces of information. The relation of the height of the station to
wthe height of the antenna is vital to the station’s later utility. The distance that the top
wof the station’s monument is found above or below the surface of the surrounding soil
wis sometimes neglected. This information cannot only be useful in later recovery of
the monument, but it can also be important in the proper evaluation of photocontrol
.Epanel points.
asyWeather
EMeteorological data are useful in modeling the atmospheric delay. This information
nis best recorded at the beginning, middle, and end of each session of projects. Under
githose circumstances, measurement of the atmospheric pressure in millibars, the rela-
netive humidity, and the temperature in degrees Celsius are expected to be included
ein the observation log. However, the general use is less stringent. The conditions of
rithe day are observed, and unusual changes in the weather are noted. A record of the
ngsatellites available during the observation and any comments about unique circum-
.netstances of the session round out the observation log.
Daily Progress Evaluation
Planned observation schedules of a large GPS project usually change daily. Arrange
ment of upcoming sessions is often altered based on the success or failure of the
previous day’s plan. Such a regrouping follows evaluation of the day’s data.
This evaluation involves examination of the observation logs as well as the data
each receiver has collected. Unhealthy data, caused by cycle slips or any other
source, are not always apparent to the receiver operator at the time of the observa-
tion. Therefore, a daily quality control check is a necessary preliminary step before
finalizing the next day’s observation schedule.
Some field supervisors prefer to actually compute the independent baseline vec-
tors of each day’s work to ensure that the measurements are adequate. Neglecting
the daily check could leave unsuccessful sessions undiscovered until the survey was
thought to be completed. The consequences of such a situation could be expensive.
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